Question

find the nature of roots of the quadratic equation 3 x square - 4√3x+ 4 =0

Answer 1

Discriminant = 96

16*9 - 3*4*4 = 96

2 distinct and real roots.

Answer 2

$3 {x}^{2} - 4 \sqrt{3} x + 4 = 0$

$here,\ a=3,\ b =-4 \sqrt{3},\ c = 4 \\ \\ Discriminant = {b}^{2} - 4ac \\ \\ D = {(-4 \sqrt{3}) }^{2} - 4 \times 3 \times 4 \\ \\ D =48 - 48 \\ \\ D =0$

$\textbf{ \red{Since D=0, the roots are real and equal.}}$